Here is a simple trick for specifying a computer in the physical world’s future inputs: run the computer for a long time, and then ask for the simplest description of the resulting sequence of inputs. The resulting description is a good predictor for future inputs, provided we live in a suitable universe.
(This is vulnerable to all of the same attacks defined in “Hazards,” and if we really want to get access to the universe as a whole, rather than just to a simulation of a single brain, it will be much harder to get around these problems.)
Now suppose we have a single bit X on a computer, and we would like to talk about the counterfactual world in which X’s value was flipped. How can we do this? Or perhaps we would like to consider an entire ensemble of possible counterfactuals in which we were given one of exponentially many possible messages m1, m2, ….
Here is one approach: consider a sequence of regularly spaced quantum coin flips F1, F2, ….. Perform each of these flips, and record the results in a list L. Continue running the computer and acquiring input I, and ensure that the result couples closely enough with the coin flips (e.g. by looking at sufficiently chaotic systems influenced by the coins, by looking at the coins directly, etc.). Then ask for the simplest function f : X -> Y such that f(L) = I. If the flips contained substantially more information than required to locate the sequence of flips in the universe, then the universe can be most concisely described by locating these distinguished coin flips and using L to determine their values (rather than by choosing them randomly, as the normal laws of physics would entail). By plugging in some other sequence of bits and asking for the computer’s inputs, we get access to the computer’s inputs in counterfactual worlds where the coin flips turned out differently.
By using these results in decision-making we can examine the results of counterfactual decisions. By using them cleverly to control input to a human, we can get around the first problem described in the post “Hazards.” But note that the other problems there still apply in force.